A common method of and apparatus for indicating characteristics of data which undulate with time is to obtain a power or energy density versus frequency response of the undulating data. It is an inherent characteristic of the power or energy density versus frequency technique to time average the energy contributions of the frequency components of a Fourier representation of the undulations in the data. It is also inherent that the power or energy density versus frequency technique neglects the relative phasing of the frequency components and thus indicates only the power or energy of the components. As a result, in certain situations undulations having different characteristics appear to have similar energy or power density versus frequency distribution. In addition, the time averaging effect has a tendency to obscure infrequently occurring events of an extreme and unusual nature so they are not well reflected in the power or energy density versus frequency analysis. Thus, in the power or energy density versus frequency analysis, the more extreme events of undulating data are regarded as statistical events in an ergodic, stochastic process in which the phasing of the frequency components is random and in which events not conforming to the normal process do not exist.
Alternatively, the undulating data peaks are regarded as those of a random variable, whereby the more extreme events conform to a certain mathematical distribution function. Because it is common for many physical processes to exhibit non-linear behavior while undergoing extreme events, a distribution function is chosen in some cases which is intended to represent the process primarily with regard to extreme values thereof. In either case, data undulations of the real process are replaced by a two-dimensional mathematical distribution function which permits a quantitative estimate of the occurrence probability of the more extreme events associated with the process. The two-dimensional nature of the distribution function permits adequate detection of extreme events primarily for narrow-band, i.e. narrow frequency range processes, because it characterizes only one quality of the process as a function of the occurrence level. The prior art techniques have, therefore, either not been applicable, or have significant limitations, for identifying unusual or "episodic" events in random, undulating data, i.e., events which tend to stand out from all other events occurring during a particular analysis interval.
Another prior art technique that has been utilized to analyze undulating data, particularly in connection with fatique lifetime estimatation, is referred to as a peak-valley or half cycle peak to peak analysis. In this prior art analysis technique, oppositely directed peak values of undulating data variations are detected. If the undulating data variation is considered as a half cycle of a wave, the oppositely directed peak values are the positive and negative maximum variations of the half cycle from a median value.
The data derived by the peak-valley technique are typically displayed as a series of numbers printed out by a digital computer. In particular, the computer printout has a format typically arranged in three columns with the titles "Range", "Peak Count" and "Valley Count". Numbers in the range column indicate the number of units between the peak and valley of each half cycle; numbers in the peak column indicate the number of half cycles having peak values in a particular range, while numbers in the valley column indicate the number of half cycles having minimum values in each of the ranges. The peak and valley data are also presented in the prior art as a sequence of maximum and minimum values supplied by a computer to a printer, such that the first maximum and minimum occur in the first and second columns of the first row of a data matrix, the maximum and minimum values of the second half cycle are presented in the third and fourth columns of the first row, etc. In this prior art technique, a dead band is provided, whereby maximum and minimum variations that occur within the dead band are not indicated. While the prior art peak-valley procedure is useful, the data are not presented in a particularly easy to handle manner, nor are certain characteristics of the undulating data immediately obvious from the data presentation.
It is, accordingly, an object of the present invention to provide a new and improved apparatus for and method of indicating characteristics of undulating data.
Another object of the invention is to provide a new and improved method of and apparatus for indicating characteristics of undulating data by employing oppositely directed peak values of variations in the data.
A further object of the invention is to provide a new and improved apparatus for and method of enabling episodic events and other non-linear characteristics of undulating data to be easily detected.
A further object of the invention is to provide a new and improved method of and apparatus for analyzing real time and stored data, to enable episodic events and other non-linear characteristics of undulating data to be easily detected.